What is the integral of 5x^2e^{6x} ?

The integral of 5x^2e^{6x} is 5(1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x}))+C

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integral of 5x^2e^{6x}

\int 5 x^{2} e^{6 x} d x

5 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})) + C

Solution steps

\int 5 x^{2} e^{6 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x^{2} e^{6 x} d x

Apply Integration By Parts

= 5 (\frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x)

\int \frac{1}{3} e^{6 x} x d x = \frac{1}{108} (6 e^{6 x} x - e^{6 x})

= 5 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}))

Add a constant to the solution

= 5 (\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})) + C

What is the integral of 5x^2e^{6x} ?
The integral of 5x^2e^{6x} is 5(1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x}))+C